動態副載波配置與適應性調變技術在多用戶多輸入多輸出正交分頻多工系統的應用

國 立 交 通 大 學

電信工程學系碩士班

碩士論文

動態副載波配置與適應性調變技術在多用

戶多輸入多輸出正交分頻多工系統的應用

Applications of Dynamic Subcarrier Allocation

and Adaptive Modulation in Multiuser

MIMO-OFDM Systems

研 究 生：王建中 Student: Jiann-Jong Wang

指導教授：李大嵩 博士 Advisor:

Dr. Ta-Sung Lee

動態副載波配置與適應性調變技術在多用戶

多輸入多輸出正交分頻多工系統的應用

Applications of Dynamic Subcarrier Allocation

and Adaptive Modulation in Multiuser

MIMO-OFDM Systems

研 究 生：王建中 Student: Jiann-Jong Wang

指導教授：李大嵩 博士 Advisor:

Dr. Ta-Sung Lee

國立交通大學

電信工程學系碩士班

碩士論文

A Thesis

Submitted to Institute of Communication Engineering

College of Electrical Engineering and Computer Science

National Chiao Tung University

in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

in

Communication Engineering

June 2004

Hsinchu, Taiwan, Republic of China

中 華 民 國 九 十 三 年 六 月

動態副載波配置與適應性調變技術在多用戶

多輸入多輸出正交分頻多工系統的應用

學生：王建中

指導教授：李大嵩 博士

國立交通大學電信工程學系碩士班

摘要

多輸入多輸出為使用多天線於傳送和接收端的可靠通訊技術，並被認為是符 合第四代高速通訊需求的最佳方案之一。透過空間多工的方式，多輸入多輸出技 術可在空間中的獨立平行通道傳送不同資料串流，藉以提昇系統的整體傳輸速 率。另一方面，正交分頻多工為一種具高頻譜效益，並能有效克服多重路徑衰減 效應的調變技術，尤其適用於多用戶系統中。在本論文中，吾人將探討結合多輸 入多輸出技術與多用戶正交分頻多工系統的通訊系統架構。基於相同副載波對於 不同用戶會展現不同通道條件的現象，吾人將針對多用戶正交分頻多工系統提出 一種動態副載波配置演算法。此演算法考慮個別用戶對於服務品質與傳輸速率不 同的需求，配置一組最適當的副載波給每一用戶，藉以提昇系統的整體傳輸速率。 此外，吾人更進一步針對多用戶多輸入多輸出正交分頻多工系統提出一種適應性 傳收架構及位元負載演算法，使系統能夠隨時間動態地在頻率與空間通道上調整 傳輸參數—例如，調變階數與傳輸能量—以便充分地利用空間、時間以及頻率通 道上的特性以維持系統的目標錯誤率，同時更進一步提昇系統的整體傳輸速率。 最後，吾人藉由電腦模擬驗證上述架構在無線通訊環境中具有優異的傳輸表現。

Applications of Dynamic Subcarrier Allocation

and Adaptive Modulation in Multiuser

MIMO-OFDM Systems

Student:

Jiann-Jong

Wang

Advisor:

Dr.

Ta-Sung

Lee

Institute of Communication Engineering

National Chiao Tung University

Abstract

Multiple-input multiple-output (MIMO) is a promising technique suited to the increasing demand for high-speed 4G broadband wireless communications. Through spatial multiplexing, the MIMO technology can transmit multiple data streams in independent parallel spatial channels, thereby increasing the total transmission rate of the system. On the other hand, orthogonal frequency division multiplexing (OFDM) is a high spectral efficiency modulation technique that can deal efficiently with multipath fading effects especially suited to multiuser systems. In this thesis, a new wireless communication system combining MIMO and multiuser OFDM system is considered, called the multiuser MIMO-OFDM system. On account of the same subcarrier experiencing different channel conditions for different users, a dynamic subcarrier allocation algorithm is proposed. This algorithm considers user-specific quality of service (QoS) and transmission rate requirements and allocates to each user the most appropriate subcarriers, thereby enhancing the overall transmission rate of the system. Furthermore, an adaptive multiuser MIMO-OFDM transceiver architecture along with a bit loading algorithm is proposed, which dynamically adjusts the transmission parameters such as modulation order and transmit power over spatial and frequency channels to fully exploit the properties of the space-time-frequency channels to meet the target bit error rate (BER) and further enhance the overall transmission rate of the system. Finally, the performance of the proposed systems is evaluated by computer simulations, confirming that they work well in wireless communication environments.

Acknowledgement

I would like to express my deepest gratitude to my advisor, Dr. Ta-Sung Lee, for his enthusiastic guidance and great patience. Heartfelt thanks are also offered to all members in the Communication Signal Processing (CSP) Lab for their constant encouragement and help. Finally, I would like to show my sincere thanks to my parents and a special friend for their inspiration and love.

Contents

Chinese Abstract

I

English Abstract

II

Acknowledgement III

Contents IV

List of Figures

VII

List of Tables

XII

Acronym Glossary

XIII

Notations XV

1 Introduction

1

2 Overview of MIMO Systems

4

2.1 MIMO System Model... 4

2.2 Channel Capacity... 7

2.2.1 SISO Channel Capacity ... 8

2.2.2 SIMO and MISO Channel Capacity ... 9

2.2.3 MIMO Channel Capacity... 10

2.3 Spatial Multiplexing ... 14

2.3.2 Vertical Bell Lab’s Layered Space-Time (V-BLAST) ...17

2.4 Computer Simulations ...20

2.5 Summary...22

3 Multiuser OFDM Systems and Subcarrier Allocation

Schemes 31

3.1 Review of OFDM ...31

3.2 Multiple Access Techniques ...36

3.3 Multiple Access in OFDM Systems...38

3.3.1 Frequency Division Multiple Access (FDMA)...39

3.3.2 Time Division Multiple Access (TDMA) ...40

3.4 Dynamic Subcarrier Allocation Algorithms for Multiuser OFDM Systems ...41

3.4.1 Basic Subcarrier Allocation Algorithm...42

3.4.2 Advanced Subcarrier Allocation Algorithm ...44

3.4.3 Two-Stage Subcarrier Allocation Algorithm ...45

3.5 Computer Simulations ...49

3.6 Summary...51

4 Multiuser Adaptive MIMO-OFDM Systems

66

4.1 V-BLAST Based OFDM Systems ...66

4.2 Adaptive Modulation for OFDM Systems...68

4.3 Switching Levels in Adaptive Modulation for OFDM Systems...70

4.4 Adaptive MIMO-OFDM Systems ...71

4.4.1 System Architecture...72

4.4.2 Two-Stage Bit Loading Algorithm...74

4.5 Computer Simulations ...80

5 Conclusion

103

List of Figures

Figure 2.1 MIMO wireless transmission system model...23

Figure 2.2 An illustration of a spatial multiplexing system ...23

Figure 2.3 Diagonal Bell Labs’ Layered Space-Time encoding procedure ...24

Figure 2.4 Diagonal Bell Labs’ Layered Space-Time decoding procedure ...24

Figure 2.5 Vertical Bell Labs’ Layered Space-Time encoding procedure...25

Figure 2.6 Vertical Bell Labs’ Layered Space-Time decoding procedure...25

Figure 2.7 Capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading SIMO channels with (Nt, Nr) = (1, 2), (1, 4), and (1, 5)...26

Figure 2.8 Capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading MISO channels with (Nt, Nr) = (2, 1), (4, 1), and (5, 1)...27

Figure 2.9 Capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading MIMO channels with (Nt, Nr) = (2, 2), (4, 4), and (5, 5) ...28

Figure 2.10 ZF V-BLAST BER performance with ideal detection and cancellation. QPSK modulation is used and (Nt, Nr) = (4, 4) ...29

Figure 2.11 ZF V-BLAST BER performance with error propagation. QPSK modulation is used and (Nt, Nr) = (4, 4)...30

Figure 3.1 OFDM signal with cyclic prefix extension...52

Figure 3.2 A digital implementation of appending cyclic prefix into OFDM signal in the transmitter...52

Figure 3.3 Black diagrams of an OFDM transceiver ...53 Figure 3.4 Illustration of different multiple access techniques (a) FDMA and

(b) TDMA ...54

Figure 3.5 OFDM time-frequency grid ...55

Figure 3.6 Illustration of block FDMA ...55

Figure 3.7 Illustration of interleaved FDMA ...56

Figure 3.8 Illustration of OFDM-TDMA...56

Figure 3.9 Flow chart of the estimation of the number of allocated subcarriers for each user ...57

Figure 3.10 Flow chart of the subcarrier assignment ...58

Figure 3.11 Channel impulse response for IEEE 802.11a ...59

Figure 3.12 A typical time-selective and frequency-selective fading channel (assuming an exponential decay channel model with 50 s rms n τ = and a speed of 60 m/s at 5 GHz) ...59

Figure 3.13 Subcarrier channel gains and corresponding number of bits for two uses under the exponential decay Rayleigh fading channel with τ_rms=50 ns, and f_d =0 Hz. Other parameters are listed in Table 3.1...60

Figure 3.14 Subcarrier channel gains for thirty users under the exponential decay Rayleigh fading channel with τ_rms=50 ns, and . Other parameters are listed in Table 3.1. ...61

0 Hz d f = Figure 3.15 Data rate versus E N for the OFDM system with the _{s 0} two-stage subcarrier allocation algorithm under the exponential decay Rayleigh fading channel with τ_rms=50 ns, and . The number of users is 10, 20, and 40. Other parameters are listed in Table 3.1...62

0 Hz d f = Figure 3.16 Data rate versus number of users for the OFDM system with different subcarrier allocation algorithms under the exponential decay Rayleigh fading channel with τ_rms=50 ns, and . Other parameters are listed in Table 3.1 ...63

0 Hz d

f =

Figure 3.17 Execution time versus number of users for the OFDM system with different subcarrier allocation algorithms under the exponential decay Rayleigh fading channel with τ_rms=50 ns, and

0 Hz d

f = . Other parameters are listed in Table 3.1 ...64

rms

τ

rms

τ

Figure 4.1 V-BLAST based MIMO-OFDM transmitter architecture ...84 Figure 4.2 V-BLAST based MIMO-OFDM receiver architecture...84 Figure 4.3 The average BER of various M-QAM modulation schemes over

AWGN channel...85 Figure 4.4 BPSK, QPSK, 8-QAM, 16-QAM, 32-QAM, and 64-QAM

constellation diagrams ...87 Figure 4.5 Block diagrams of the multiuser adaptive MIMO-OFDM system ...88 Figure 4.6 V-BLAST based multiuser adaptive MIMO-OFDM transmitter

acchitecture ...88 Figure 4.7 V-BLAST based multiuser adaptive MIMO-OFDM receiver

architecture...89 Figure 4.8 Flow chart of the first stage adaptive bit loading algorithm. .…...89 Figure 4.9 Simulated probabilities of each modulation mode utilized by the

ZF V-BLAST based multiuser adaptive MIMO-OFDM system (with space-frequency loading) under the exponential decay Rayleigh fading channel with τ_rms= 50 ns, and f_d =0 Hz. (Nt, Nr) = (4, 4). The number of users is 10. Other parameters are

listed in Table 4.2...90 Figure 4.10 BER versus E N for the ZF V-BLAST based multiuser _{s 0}

adaptive MIMO-OFDM system without using residual power. The exponential decay Rayleigh fading channel is employed with

=50 ns, and f_d =0 Hz. (Nt, Nr) = (3, 3), (4, 4), and (4, 5).

The number of users is 10. Other parameters are listed in Table

4.2 ...91 Figure 4.11 BER versus E N for the MMSE V-BLAST based multiuser _{s 0}

adaptive MIMO-OFDM system without using residual power. The exponential decay Rayleigh fading channel is employed with

The number of users is 10. Other parameters are listed in Table

4.2 ...92 Figure 4.12 BER versus E N for the ZF V-BLAST based multiuser _{s 0}

adaptive MIMO-OFDM system using residual power. The exponential decay Rayleigh fading channel is employed with

rms

τ =50 ns, and f_d =0 Hz. (Nt, Nr) = (3, 3), (4, 4), and (4, 5).

The number of users is 10. Other parameters are listed in Table

4.2 ...93 Figure 4.13 Simulated probabilities of each modulation mode utilized by the

ZF V-BLAST based multiuser adaptive MIMO-OFDM system (with space-frequency and space loading, respectively) under the exponential decay Rayleigh fading channel with τ_rms= 50 ns, and f_d =0 Hz. (Nt, Nr) = (4, 4). The number of users is 10.

Other parameters are listed in Table 4.2 ...94 Figure 4.14 Data rate versus E N_{s 0}

rms

for the ZF V-BLAST based multiuser adaptive MIMO-OFDM system (with space-frequency and space loading, respectively) under the exponential decay Rayleigh fading channel with τ = 50 ns, and f_d =0 Hz. (Nt, Nr) =

(3, 3), (4, 4), (4, 5), and (5, 5). The number of users is 10. Other

parameters are listed in Table 4.2 ...95 Figure 4.15 Simulated probabilities of each modulation mode utilized by the

ZF V-BLAST based multiuser adaptive MIMO-OFDM system (with space-frequency loading) under the exponential decay Rayleigh fading channel with τ_rms= 50 ns, and f_d =0 Hz. (Nt, Nr) = (4, 4), (4, 5), and (5, 5). The number of users is 10.

Other parameters are listed in Table 4.2 ...96 Figure 4.16 Data rate versus E N for the ZF V-BLAST based multiuser _{s 0}

adaptive MIMO-OFDM system (with space-frequency loading) under the exponential decay Rayleigh fading channel with τ_rms= 50 ns, and f_d = Hz0 . (Nt, Nr) = (3, 3), (3, 4), (3, 5), (4, 4), (4, 5),

in Table 4.2...97 Figure 4.17 Unutilized power ratio versus E N for the ZF V-BLAST _{s 0}

based multiuser adaptive MIMO-OFDM system (with space-time loading) under the exponential decay Rayleigh fading channel with τ_rms= 50 ns, and f_d =0 Hz. (Nt, Nr) = (3, 3), (4, 4), (4, 5),

and (5, 5). The number of users is 10. Other parameters are listed

in Table 4.2...98 Figure 4.18 Bit rate versus E N for the ZF V-BLAST based multiuser _{s 0}

adaptive MIMO-OFDM system with different bit loading algorithms under the exponential decay Rayleigh fading channel with τ_rms= 50 ns, and f_d =0 Hz. (Nt, Nr) = (4, 4). The number

of users is 10. Other parameters are listed in Table 4.2 ...99 Figure 4.19 BER versus E N for the V-BLAST based multiuser adaptive _{s 0}

MIMO-OFDM system using residual power with different detection criteria. The exponential decay Rayleigh fading channel is employed with τ_rms= 50 ns, and f_d =0 Hz. (Nt, Nr)

= (4, 4). ΔH is equal to the noise power. The number of users is

10. Other parameters are listed in Table 4.2 ...100 Figure 4.20 BER versus E N for the ZF V-BLAST based multiuser _{s 0}

adaptive MIMO-OFDM system under the exponential decay Rayleigh fading channel with τ_rms= 50 ns. . v = 120, 60, 30, and 6 m/s. The number of users is 10. Other parameters are listed in Table 4.2 ...101

List of Tables

Table 3.1 Simulation parameters for the OFDM system ... 65

Table 4.1 SNR threshold table for various M-QAM at the target BER=10-4...102 Table 4.2 Simulation parameters for the proposed V-BLAST based

Acronym Glossary

ADC analog-to-digital conversion

AWGN additive white Gaussian noise

BER bit error rate

BLAST Bell Lab Layered space time BPSK binary phase shift keying

BS base station

CCI co-channel interference

CNR channel gain-to-noise ratio

CP cyclic prefix

CRC cyclic redundancy check

CSI channel state information

D-BLAST diagonal Bell labs’ layered space-time

DFT discrete Fourier transform

FDMA frequency division multiple access

FFT fast Fourier transform

FSK frequency shift keying

ICI intercarrier interference

IEEE institute of electrical and electronics engineers IFFT inverse fast Fourier transform

ISI intersymbol interference

LOS line of sight

MAI multiple access interference

MCM multicarrier modulation

MIMO multiple-input multiple-output

MMSE minimum mean square error

MS mobile station

OFDM orthogonal frequency division multiplexing

PER packet error rate

QAM quadrature amplitude modulation

QoS quality of service

QPSK quaternary phase shift keying

RF radio frequency

SD spatial diversity

SDR software defined radio

SIMO single-input multiple-output

SISO single-input single-output

SM spatial multiplexing

SNR signal-to-noise ratio

STC space-time coding

SVD singular value decomposition

TDD time division duplex

TDMA time division multiple access

V-BLAST vertical Bell laboratory layered space-time

WF water filling

Notations

C channel _capacity b E bit energy s E symbol energy , i j

h channel gain between the jth transmit and ith receive antenna M modulation order

c

N number of subcarriers cp

N number of guard interval samples t

N number of transmit antenna r

N number of receive antenna

0

N noise power spectrum density budget

P power budget

q antenna state

S set of signal constellation T set of switching levels

s

T symbol duration

sample

T sampling period

k

w weighting vector for the kth layer

2 n σ noise power error ε target BER γ instantaneous SNR rms

τ root mean squared excess delay spread

ρ average SNR at each receive antenna λ eigenvalue

Chapter 1

Introduction

The increasing popularity of enhanced communication services, such as wireless multimedia, telecommuting, fast Internet access, and video conferencing, has promoted the growing demand of high data rate, high mobility, and high quality of service (QoS) requirements for users. However, the limited available bandwidth drives the wireless communication technology towards the emerging issue of high spectral efficiency. Besides, in wireless channels, the time-selective and frequency-selective fading caused by multipath propagation, carrier frequency/phase shift, and Doppler shift limit the developments of high data rate and reliable communications. As a remedy, some efficient modulation and coding schemes such as coded multicarrier modulation, multiple-input multiple-output (MIMO) technology [1]-[12], and adaptive resource allocation [13]-[17] are proposed to enhance the spectral efficiency and quality of wireless communication links.

MIMO techniques, i.e., a radio communication system equipped with multiple antenna elements at both the transmitting end and receiving end, have been demonstrated to effectively increase the transmission capacity and support high data rate. The signals on the transmit antennas at one end and on the receive antennas at the other end are “co-processed” in such a way that the quality or the data rate of the communication link can be improved. The core idea of MIMO systems is the space-time signal processing in which time is complemented with the spatial dimension inherent in the use of multiple spatially distributed antennas. Furthermore, the key feature of MIMO systems is to efficiently exploit the multipaths, rather than mitigate

them, to achieve the signal decorrelation necessary for separating the co-channel signals. Specifically, the multipath phenomenon presents itself as a source of diversity that takes advantage of random fading.

The high data rate wireless transmission over the multipath fading channels is mainly limited by intersymbol interference (ISI). Orthogonal frequency division multiplexing (OFDM) [18]-[19] has been considered as a reliable technology to deal with the ISI problem. The principle of the OFDM technology is to split a high data rate stream into a number of low data rate streams which are simultaneously transmitted on a number of orthogonal subcarriers. By adding a cyclic prefix (CP) to each OFDM symbol, both intersymbol and intercarrier interference can be removed and the channel also appears to be circular if the CP length is longer than the channel length. The multicarrier property of OFDM systems can not only improve the immunity to fast fading channels, but also make multiple access possible because the subcarriers are independent of each other.

OFDM combining antenna arrays at both the transmitter and receiver, which leads to a MIMO-OFDM configuration, can significantly increase the diversity gain or enhance the system capacity over time-variant and frequency-selective channels. Typical MIMO-OFDM systems can be categorized into two types: those based on spatial multiplexing (SM) [1], [20] and those based on spatial diversity (SD) schemes. The former system is a layered spatial transmission scheme, in which different data streams are transmitted from different transmit antennas simultaneously and received through nulling and canceling to mitigate the co-channel interference (CCI). The latter one uses space-time coding (STC) techniques to improve the transmission reliability. STC can provide diversity gain and increase the effective transmission rate without sacrificing the bandwidth.

In the multiuser MIMO-OFDM system, each of the multiple users’ signals may undergo independent fading due to different locations of users. Therefore, the subcarriers in deep fade for one user may not be in the same fade for other users. In fact, it is quite unlikely that a subcarrier will be in deep fade for all users. Hence, for a specific subcarrier, the user with the best channel quality can use the subcarrier to transmit data yielding multiuser diversity effects [21]. Recently, methods for

dynamically assigning subcarriers to each user have been widely investigated [23]-[24]. These dynamic subcarrier allocation algorithms can be geared to decrease the power consumption for a given achievable data rate or to increase the data rate when the available power is limited. In this thesis, a dynamic subcarrier allocation algorithm suited to the multiuser OFDM system is developed to take both user-specific data rate and quality of service (QoS) requirements into account and allocate to each user the most appropriate subcarriers.

As the instantaneous channel state information (CSI) is determined beforehand, the multiuser MIMO-OFDM system incorporating the adaptive modulation technique can provide a significant performance improvement. Adaptive modulation can dynamically adjust transmission parameters to alleviate the effects of channel impairments. Subcarriers with good channel qualities can employ higher modulation order to carry more bits per OFDM symbol, while subcarriers in deep fade may employ lower modulation order or even no transmission. In addition, the adaptive modulation technique must take into account the additional signaling dimensions explored in future broadband wireless networks [16]. More specifically, the growing popularity of both MIMO and multiuser OFDM systems creates the demand for link adaptation solutions to integrate temporal, spectral, and spatial components together. In this thesis, an adaptive wireless transceiver is developed to effectively exploit the available degrees of freedom in wireless communication systems.

This thesis is organized as follows. In Chapter 2, the general system model and channel capacity of a MIMO communication link are described. In Chapter 3, the multiple access concepts of the multiuser OFDM system are introduced and a dynamic subcarrier allocation algorithm is proposed which allows users to choose the most appropriate subcarriers according to their requirements and the channel qualities. In Chapter 4, the adaptive modulation concepts are introduced and an adaptive bit loading algorithm suited to the multiuser MIMO-OFDM system is proposed to further increase the total transmission rate and still meet the target bit error rate (BER). Finally, Chapter 5 gives concluding remarks of this thesis and leads the way to some potential future works.

Chapter 2

Overview of MIMO Systems

Digital communication using multiple-input multiple-output (MIMO) has recently emerged as one of the most significant technical breakthroughs in wireless communications. The technology figures prominently on the list of recent technical advances with a chance of resolving the bottleneck of traffic capacity in future Internet intensive wireless networks. In this chapter, the basic ideas and key features of the MIMO system will be introduced.

2.1 MIMO

System

Model

MIMO system architectures provide substantially better spectral efficiency than traditional systems. With this transmission scheme, there is a linear increase in spectral efficiency compared to a logarithmic increase in traditional systems utilizing receive diversity. The increase in spectral efficiency is based on the utilization of antenna or space diversity both at the transmitter and receiver sides in MIMO systems.

A key feature of MIMO systems is the ability to turn multipath propagation, traditionally a pitfall of wireless transmission, into a benefit for the user. MIMO systems effectively take advantage of random fading and multipath delay spread for multiplying transfer rates. In a rich scattering environment, the signals transmitted from each transmit antenna appear highly uncorrelated at each receive antenna. When the transmitter transmits signals to the receiver through uncorrelated channels, the signals from each transmit antenna obtain different spatial signatures. Then the receiver can exploit these different spatial signatures to separate the signals transmitted from

different transmit antennas but at the same frequency band simultaneously.

MIMO systems can be defined simply. Given an arbitrary wireless communication system, a link is considered for which the transmitting end is equipped with transmit antennas and receiving end is equipped with receive antennas. Such a setup is illustrated in Fig. 2.1.

t N

r

N

Consider a communication link comprising transmit antennas and receive antennas that contributes to a MIMO channel, as shown in Fig. 2.1. Some important assumptions are made firstly:

t

N N_r

1. The channel is constant during the transmission of a packet. It means the communication is carried out in packets that are of shorter time-span than the coherence time of the channel.

2. The channel is memoryless. It means that an independent realization of channel is drawn for each use of the channel. It also means that the channel capacity can be computed as the maximum of the mutual information as defined in Equation (2.6). 3. The channel is frequency-flat fading. It means that constant fading over the

bandwidth is deserved when the case of narrowband transmission is dealt with. It also indicates that the channel gain can be represented as a complex number. 4. Only a single user transmits signals at any given time, so the received signal is

corrupted by AWGN only.

With these assumptions, it is common to represent the input/output relations of a narrowband, single user MIMO link by the complex baseband vector notation

y = Hx + n (2.1)

where is the x N_t×1 transmit vector, y is the N_r×1 receive vector, is the channel matrix, and is the

H

r

N ×N_t n N_r×1 additive white Gaussian noise (AWGN)

vector at a given instant in time. All of the coefficients comprise the channel matrix . The coefficient represents the complex gain of the channel between the jth transmit antenna and the ith receive antenna.

ij

h

H h_ij

11 12 1 21 22 2 1 2 t t r r r N N N N N N h h h h h h h h h      =_       H … … t   (2.2) where 1 tan 2 2 = = ij ij ij ij ij ij j ij ij j ij h j e h e β α φ α β α β − − = + + ⋅ ⋅ (2.3)

The coefficients {hij} stand for unknown transmission properties of the medium,

usually Rayleigh distributed in a rich scattering environment with no line-of-sight (LOS). If α and β are independent and Gaussian distributed random variables, then

ij

h is a Rayleigh distributed random variable. In fact, the coefficients {hij} are likely

to be subject to varying degrees of fading and change over time. Therefore, the determination of the channel matrix is an important and necessary aspect of MIMO processing. If all these coefficients are known, there will be sufficient information for the receiver to eliminate interference from other transmitters operating at the same frequency band. At the beginning, the channel matrix is estimated using a well-designed preamble training sequences sent ahead of the payload. Then the channel matrix is refined dynamically using pilot tones that are sent in conjunction with the payload. Moreover, when comparing the systems equipped with different N

H

t and Nr

antennas, the channel matrix H has to be normalized. The channel matrix is normalized

such that H 2_F =N N_t⋅ _r , where 2_F represents the Frobenius norm. This normalization step keeps the spatial characteristics but removes the influence of the time and frequency variation. There are some MIMO channel estimation methods proposed, which can be found in [10], [24].

2.2 Channel

Capacity

A measure of how much information that can be transmitted and received with a negligible probability of error is called the channel capacity. To determine this measure of channel potential, a channel encoder receiving a source symbol every Ts second is

assumed. If S represents the set of all source symbols and the entropy rate of the source is written asH s( ), the channel encoder will receive H(s)/Ts information bits per second

on average. A channel codeword leaving the channel encoder every Tc second is also

assumed. In order to be able to transmit all the information from the source, there must be R information bits per channel symbol.

( ) _c s H s T R T = (2.4)

The number R is called the information rate of the channel encoder. The maximum information rate that can be used causing negligible probability of errors at the output is called the capacity of the channel. By transmitting information with the rate R, the channel is used every Tc seconds. The channel capacity is then measured in bits per

channel use. Assuming that the channel has bandwidth W, the input and output can be represented by samples taken Ts = 1/2W seconds apart. With a band-limited channel,

the capacity is measured in information bits per second. It is common to represent the channel capacity within a unit bandwidth of the channel, which means that the channel capacity is measured in bits/sec/Hz.

It is desirable to design transmission schemes that exploit the channel capacity as much as possible. Representing the input and output of a memoryless wireless channel with the random variables X and Y respectively, the channel capacity is defined as

( )

(

)

max ; bits/sec/Hz

p x

C= I X Y (2.5)

where ( ; )I X Y represents the mutual information between X and Y. Equation (2.5) states that the mutual information is maximized when considering all possible transmitter statistical distributions p(x). Mutual information is a measure of the amount of information that one random variable contains about another one. The mutual information between X and Y can also be written as

( ; ) ( ) ( | )

I X Y =H Y −H Y X (2.6)

where represents the conditional entropy between the random variables X and Y. The entropy of a random variable can be described as a measure of the uncertainty of the random variable. It can also be described as a measure of the amount of information required on average to describe the random variable. Due to Equation (2.6), mutual information can be described as the reduction in the uncertainty of one random variable due to the knowledge of the other. Note that the mutual information between X and Y depends on the properties of X (through the probability distribution of X) and the properties of channel (through a channel matrix H). In the following, four

different kinds of channel capacities are introduced (single-input single-output (SISO), single-input multiple-output (SIMO), multiple-input single-output (MISO), and MIMO) to get the further concepts about the properties of the channel capacity.

( | ) H Y X

2.2.1 SISO Channel Capacity

The ergodic (mean) capacity of a random channel (Nt = Nr = 1) with the average

transmit power constraint PT can be expressed as

( )

(

)

{

max: T ;

}

bits/sec/Hz H _{p x P P} C E I X Y ≤ = (2.7)

where EH denotes the expectation over all channel realizations and P is the average

power of a single channel codeword transmitted over the channel. Compared to the definition in Equation (2.5), the capacity of the channel is now defined as the maximum of the mutual information between the input and output over all statistical distributions on the input that satisfy the power constraint. If each channel symbol at the transmitter is denoted by s, the average power constraint can be expressed as

2 T

P E s= _ _≤P (2.8)

Using Equation (2.7), the ergodic (mean) capacity of a SISO system (Nt = Nr = 1) with

a random complex channel gain h11 is given by

(

)

{

2

}

2 11 log 1 bits/sec/Hz H C E= + ⋅ρ h (2.9)

where ρ is the average signal-to-noise (SNR) ratio at the receive branch. If |h11| is

Rayleigh, |h11|2 follows a chi-squared distribution with two degrees of freedom.

Equation (2.7) can then be written as

(

)

{

2

}

2 2 log 1 bits/sec/Hz H C E= + ⋅ρ χ (2.10)

where χ22 is a chi-square distributed random variable with two degrees of freedom.

2.2.2 SIMO and MISO Channel Capacity

As more antennas deployed at the receiving end, the statistics of capacity improve. Then the ergodic (mean) capacity of a SIMO system with Nr receive antennas is given

by 2 2 1 1 log (1 Nr _i ) bits/sec/Hz i C ρ h = = +

_∑

(2.11)

where hi1 represents the gain for the receive antenna i. Note that the crucial feature in

Equation (2.11) is that increasing the number of receive antennas Nr only results in a

logarithmic increase in the ergodic (mean) capacity. Similarly, if transmit diversity is opted, in the common case, where the transmitter doesn’t have the channel knowledge, the ergodic (mean) capacity of a MISO system with Nt transmit antennas is given by

2 2 1 1 log (1 Nt _i ) bits/sec/Hz i t C h N ρ = = +

_∑

(2.12)

where the normalization by Nt ensures a fixed total transmit power and shows the

absence of array gain in that case (compared to the case in Equation (2.11), where the channel energy can be combined coherently). Again, the capacity has a logarithmic relationship with the number of transmit antennas Nt.

2.2.3 MIMO Channel Capacity

The capacity of a random MIMO channel with the power constraint PT can be

expressed as ( ) ( )

( )

{

max: T ;

}

bits/sec/Hz H _{p tr P} C E I Φ ≤ = x x y (2.13)

where is the covariance matrix of the transmit signal vector x. By the

relationship between mutual information and entropy and using Equation (2.1), Equation (2.13) can be expanded as follows for a given channel matrix H.

2 { H} E xx = Φ

( )

( ) (

)

( ) (

)

( ) (

)

( ) ( )

; | | | I h h h h h h h h = − = − + = − = − x y y y x y Hx n x y n x y n (2.14)

where denotes the differential entropy of a continuous random variable. It is assumed that the transmit vector x and the noise vector n are independent.

( )

h ⋅

When y is Gaussian, Equation (2.14) is maximized. Since the normal distribution

maximizes the entropy for a given variance. The differential entropy of a complex Gaussian vector y ∈ Cn_{, the differential entropy is less than or equal to ,}

with equality if and only if y is a circularly symmetric complex Gaussian with

. For a real Gaussian vector y ∈ R

(

)

2

log det πeK

{ H}

E yy = K n _{with zero mean and covariance matrix,}

K is equal to lo . Assuming the optimal Gaussian distribution for the transmit vector x, the covariance matrix of the received complex vector y is given by

(

2 g (2 ) det_πe n _K

)

/ 2

{ }

{

(

)(

)

}

{

} { }

H H H H H H n d n E E E E = + + = + = + = + yy Hx n Hx n Hxx H nn HΦH K K K (2.15)

The desired part and the noise part of Equation (2.15) denotes respectively by the superscript d and n. The maximum mutual information of a random MIMO channel is then given by

( ) ( )

(

)

(

)

(

)

(

)

( )

(

)( )

(

)

( )

(

)

( )

(

)

2 2 2 2 1 2 1 2 1 2

log det log det

log det log det

log det log det log det d n n d n n d n n d n M H n M I h h e e π π − − − = −     = _ + _− _{ }     = _ + _− _{ }   = _ + _     = _ + _     = _ + _   y n K K K K K K K K K K K I HΦH K I (2.16)

When the transmitter has no knowledge about the channel, it is optimal to use a uniform power distribution. The transmit covariance matrix is then given by

. It is also common to assume uncorrelated noise in each receive antenna described by the covariance matrix

/ t T N t P Φ = I N 2 r n N σ =

K I . The ergodic (mean) capacity for a complex additive white Gaussian noise (AWGN) MIMO channel can then be expressed as

2 2

log det _r T H bits/sec/Hz

H N t P C E N σ      = _{  } + _       I HH    (2.17)

Equation (2.17) can also be written as

2

log det _r H bits/sec/Hz

H N t C E N ρ       = _{  } + _       I HH  (2.18) where _/ 2 T P

ρ = σ is the average signal-to-noise (SNR) at each receive antenna. By the law of large numbers, the term H / _r as N

t

N →

HH I_N r is fixed and Nt gets large.

Hence the capacity in the limit of large transmit antennas Nt can be written as

(

)

{

log 12

}

bits/sec/Hz

H r

C E= N ⋅ +ρ (2.19)

Further analysis of the MIMO channel capacity given in Equation (2.18) is possible by diagonalizing the product matrix either by eigenvalue decomposition or singular value decomposition (SVD). By using SVD, the matrix product is written as

H

H

=

H UΣV (2.20)

where U and V are unitary matrices of left and right singular vectors respectively, and Σ is a triangular matrix with singular values on the main diagonal. All elements on the diagonal are zero except for the first k elements. The number of non-zero singular values k of Σ equals the rank of the channel matrix. Substituting Equation (2.20) into Equation (2.18), the MIMO channel capacity can be written as

2

log det _r H H bits/sec/Hz

H N t C E I N ρ      = _{  } + _       UΣΣ U    H (2.21)

The matrix product can also be described by using eigenvalue decomposition on the channel matrix H written as

H

HH

H ₌

HH EΛE (2.22)

where E is the eigenvector matrix with orthonormal columns and Λ is a diagonal matrix with the eigenvalues on the main diagonal. Using this notation, Equation (2.18) can be written as

2

log det _r H bits/sec/Hz

H N t C E N ρ       = _{  } + _       I EΛE  (2.23)

After diagonalizing the product matrix , the capacity formulas of the MIMO channel now includes unitary and diagonal matrices only. It is then easier to see that the total capacity of a MIMO channel is made up by the sum of parallel AWGN SISO subchannels. The number of parallel subchannels is determined by the rank of the channel matrix. In general, the rank of the channel matrix is given by

H

HH

( ) min( _t, _r)

rank H = ≤k N N (2.24)

Using the fact that the determinant of a unitary matrix is equal to 1 and Equation (2.24), Equations (2.21) and (2.23) can be expressed respectively as

2 2 1 log 1 bits/sec/Hz k H i i t C E Nρ σ =      = _{ } + _    

∑

 (2.25)

2 1 log 1 bits/sec/Hz k H i i t E Nρ λ =      = _{ } + _    

∑

 (2.26)

where σi2 are the squared singular values of the diagonal matrix Σ and λi are the

eigenvalues of the diagonal matrix Λ. The maximum capacity of a MIMO channel is achieved in the unrealistic situation when each of the Nt transmitted signals is received

by the same set of Nr antennas without interference. It can also be described as if each

transmitted signal is received by a separate set of receive antennas, giving a total number of N N_t⋅ _r receive antennas.

With optimal combining at the receiver and receive diversity only (Nr = 1), the

channel capacity can be expressed as

(

)

{

2

}

2 2 log 1 bits/sec/Hz r H N C E= + ⋅ρ χ (2.27) where 2 2Nr

χ is a chi-distributed random variable with 2Nr degrees of freedom. If there

are Nt transmit antennas and optimal combining between Nr antennas at the receiver,

the capacity can be written as

2 2 2 log 1 _r bits/sec/Hz H t N t C E N Nρ χ      = _ ⋅ _ + ⋅ _      (2.28)

Equation (2.28) represents the upper bound of a Rayleigh fading MIMO channel. When the channel is known at the transmitter, the maximum capacity of a MIMO channel can be achieved by using the water-filling (WF) principle on the transmit covariance matrix. The capacity is then given by

2 1 2 2 1 2 1 log 1 log 1 log ( ) bits/sec/Hz k H i i t k H i i t k i i C E N E N u ρ ε λ ρ ε σ λ = = + =      = _{ } + _          = _{ } +      =

∑

∑

∑

i i    (2.29)

where “+” denotes taking only those terms which are positive and u is a scalar, representing the portion of the available transmit power going into the ith subchannel which is chosen to satisfy

1 1 ( k i i u ρ λ− + = =

∑

− ) (2.30)

Since u is a complicated nonlinear function of λ λ₁, ₂,…,λ_k, the distribution of the channel capacity appears intractable, even in the Wishart case when the joint distribution of λ λ₁, ₂,…,λ_k is known. Nevertheless, the channel capacity can be simulated using Equations (2.29) and (2.30) for any given so that the optimal capacity can be computed numerically for any channel [12].

H

HH

2.3 Spatial

Multiplexing

The use of multiple antennas at both ends of a wireless link has recently been shown to have the potential of achieving extraordinary data rate. The corresponding technology is known as spatial multiplexing [1]-[3], [11]. It allows a data rate enhancement in a wireless radio link without additional power or bandwidth consumption. In spatial multiplexing systems, different data streams are transmitted from different transmit antennas simultaneously or sequentially and these data streams are separated and demultiplexed to yield the original transmitted signals according to their unique spatial signatures at the receiver. An illustration of the spatial multiplexing system is shown in Fig. 2.2. The separation step is made possible by the fact that the rich scattering multiplath contributes to lower correlation between MIMO channel coefficients, and creates a desirable full rank and low condition number coefficient matrix condition to resolve Nt unknows from a linear system of Nr equations. In the

following, two typical spatial multiplexing schemes, D-BLAST [1] and V-BLAST [3], [11], are introduced.

2.3.1 Diagonal Bell Lab’s Layered Space-Time

(D-BLAST)

Space-time coding (STC) performs channel coding across space and time to exploit the spatial diversity offered by MIMO systems to increase system capacity. However, the decoding complexity of the space-time codes is exponentially increased with the number of transmit antennas, which makes it hard to implement real-time decoding as the number of antennas grows. To reduce the complexity of space-time based MIMO systems, D-BLAST architecture has been proposed in [1]. Rather than try to achieve optimal channel coding scheme, in D-BLAST architecture, the input data stream is divided into several substreams. Each substream is encoded independently using an elegant diagonally-layered coding structure in which code blocks are dispersed across diagonals in space-time and the association of corresponding output stream with transmit antenna is periodically cycled to explore spatial diversity. To decode each layer, channel parameters are used to cancel interference from undetected signals to make the desired signal as “clean” as possible.

Fig. 2.3 shows the typical encoding steps in D-BLAST. Considering a system with Nt transmit and Nr receive antennas, the high rate information data stream is first

demultiplexed into Nt subsequences. Each subsequence is encoded by a conventional

1-D constituent code with low decoding complexity. The encoders apply these coded symbols to generate a semi-infinite matrix C of Nt rows to be transmitted. The element

in the pth row and column of C, , is transmitted by the pth transmit antenna at time . As illustrated in Fig. 2.2, are encoded by encoder α,

are encoded by encoder β, and are encoded by

encoder γ. th t p t c t , , 1 2 3 1 2 3 1, , , , ,2 3 4 5 6 c c c c c c c c 1 2 3 1 2 3 2 3 4, , ,5 6 7 c c c c c c 1 2 3 1 2 3 3, , , , ,4 c c c c5 6 7 8

Fig. 2.4 shows the typical decoding steps of interference suppression, symbol detection, decoding, and interference cancellation performed in D-BLAST. The receiver generates decisions for the first diagonal of C. Based on these decisions, the diagonal is decoded and fed back to remove the contribution of this diagonal from the received data. The receiver continues to decode the next diagonal and so on. The encoded substreams share a balanced presence over all paths to the receiver, so none of

the individual substreams is subject to the worst path. Therefore, the data received at time by the qth receive antenna is t , which contains a superposition of c ,

2 q t r p t 1, , , _t

p= … N , and an AWGN noise component. Then, the received data vector can be expressed as r_t =H c_{t t} +ξ_t at any time instance . The D-BLAST method uses a repeated process of interference suppression, symbol detection, and interference cancellation to decode all symbols, . This decoding process can be expressed in a general form described in the following.

t 1 c 1_,..., t, t− N N t t c c _t

Let Q R_{t t} be the QR decomposition of , where is an N t

R

t

H Q_t r × Nr unitary

matrix and is an Nr × Nt upper triangular matrix. Multiplying the received signal

by H t Q , we can get Nr t H H H H H t t t t t t t t t t t t t t t t = = + = + = + I ξ y Q r Q H c Q ξ Q Q R c Q ξ_t R c ξ (2.31) where 1, 1,1 1,2 2, 2,2 1 1 2 2 , 0 0 0 , ,0 0 0 0 0 0 0 0 t t t t r r N t t t N t t t t t N N t t t t t N N t t r r r r r y y r y ξ ξ ξ       _{ }     _{ }     _{ }   = =_{ } =       _{ }                   y R ξ (2.32)

Since R_t is a upper triangular matrix, the elements in the vector y can be expressed _t

as

{

}

, p _{contribution from c , ,...,} Nt p p p p p p t t t t t t t y =r c +ξ + +1 c +2 c _(2.33)

Hence, the interference from q, t

c q< ≤p N_t, is first suppressed in and the residual interference terms in Equation (2.33) can be cancelled by the available

decisions , ,…, k t y 1 ˆp c_τ+ _cˆp 2

τ+ cˆτNt. Assuming all these decisions are correct, then the present

, _{, 1,2, ,}

p p p p p

t t t t

c =r c +ξ p= … N_t (2.34)

The relation between and c in Equation (2.34) can be interpreted as the input and output of a SISO channel with the channel power gain

p

c p

2 ,

p p

r and AWGN. The channel power gain _rp p, 2 _{is independently chi-squared distributed with 2×(N}

r−p+1)

degrees of freedom. Moreover, if there are no decision feedback errors, the pth row of the C matrix can be treated as transmitted over a (Nt, Nr)=(1, Nr−p+1) system without

interference from the other rows and all fades are i.i.d.

2.3.2 Vertical Bell Lab’s Layered Space-Time

(V-BLAST)

The D-BLAST algorithm has been proposed by Foschini for achieving a substantial part of the MIMO capacity. In an independent Rayleigh scattering environment, this processing structure leads to theoretical rates which grow linearly with the number of antennas (assuming equal number of transmit and receive antennas) with these rates approaching ninety percents of Shannon capacity. However, the diagonal approach suffers from certain implementation complexities which make it inappropriate for practical implementation. Therefore, a simplified version of the BLAST algorithm is known as V-BLAST (vertical BLAST) [3], [11]. It is capable of achieving high spectral efficiency while being relatively simple to implement. The essential difference between D-BLAST and V-BLAST lies in the vector encoding process. In D-BLAST, redundancy between the substreams is introduced through the use of specialized intersubstream block coding. In V-BLAST, however, the vector encoding process is simply a demultiplex operation followed by independent bit-to-symbol mapping of each substream. No intersubstream coding, or coding of any kind, is required, though conventional coding of the individual substreams will certainly be applied.

Fig. 2.5 shows the typical encoding steps in V-BLAST. The coding procedure can be viewed as there is an encoder on each transmit antenna. The output coded symbols of one encoder are transmitted from the corresponding transmit antenna. The output

coded symbol of the pth encoder is used to fill the pth row of C.

Fig. 2.6 shows the typical decoding steps in V-BLAST. The detection procedure is to extract the strongest substream from the signals received by the all receive antennas simultaneously. Then, the procedure proceeds with the remaining weaker signals, which are easier to recover when the strongest signals have been removed as a source of interference. Following the data model in D-BLAST, let l 1

t = ₌ H H r j l k and at

the first decoding step at a given time instant . In each step l, the pseudo-inverse of is calculated to be the nulling matrix .

1 l t = ₌ r t l H _Gl

(

)

1 ( ) ( ) ( ) l l l H l l H + − = = G H H H H (2.35)

Each row of can be used to null all but the lth desired signal. The layer shows the biggest post-processing SNR suggested to be detected first to reduce the error propagation effect efficiently [3]. At this step, the row of with the minimum norm is chosen and the corresponding row is defined as the nulling vector .

l G l G l T k w {1 1} 2 ,..., arg min || ( ) || l l l j k k k − ∉ = G (2.36) ( ) l l T k = w G (2.37)

The post-processing SNR for the klth detected component of c can be defined as

2 2 | | || || l l l k k k c ρ σ < > = w 2 (2.38)

Then, using to suppresses all layers but the one transmitted from antenna and a soft decision value is obtained

l k w k_l l l k T l t k c = w r_t (2.39)

Therefore, the k_lth layer can be detected within the constellation set S

2 ˆkl arg min || kl || t x S c c ∈ = −c_t (2.40)

As soon as one layer is detected, the part of the detected signal can be subtracted from the received vector to improve the detection performance for the later layers.

( )

1 _ˆkl kl l l l t t ct + _{= −} r r H (2.41) where

( )

_l kl

H denotes the klth column of . Then, the channel matrix is deflated to

account for its removal.

l H

( )

1 kl l+ ₌ H Hl _(2.42)

where the notation

( )

_l kl

H denotes the matrix obtained by zeroing columns

of . Therefore, the diversity gain is increased by one at each step when we decrease the number of layers to be nulled out in the next step by one.

1, ,...,2 l

k k k

l

H

The Zero-Forcing (ZF) V-BLAST detection algorithm can be summarized as follows: Initialization:

( )

1 1 1 2 1 1 arg min || ( ) ||_j j i k + ← = = G H G Recursion:

( )

( )

{1 } 1 1 +1 1 1 2 1 _, ( ) ˆ ( ) ˆ ( ) arg min || ( ) || 1 l l l l l l l l l l l l l T k k k T l k k T l k k k k k l l l k l l l l l l _{j k k} j c c c Q c c k i i + + + + + + _∉ = = = = = − = = = ← + w G w r w r r r H H H G H G

ZF one, it can improve the detection performance especially for the mid-range SNR values [3]. 1 1 ( ) ( ) l l H l l SNR −   =_ + _   G H H I H H _(2.43)

In the MMSE detection case, the noise level on the channel is taken into account besides nulling out the interference. Thus, the SNR has to be estimated at the receiver.

2.4 Computer

Simulations

First, the capacity of a SISO channel compared with different kinds of Rayleigh fading channel scenarios such as SIMO, MISO, and MIMO channels are simulated. Second, the ZF V-BLAST BER performances for the ideal detection and cancellation case and with error propagation case are simulated. In simulations, the relationship between SNR and E N_{b 0} can be defined as

(

0 0 0 signal power SNR 1 noise power s b t s s b t s E E N M T T E N M N B _N N T

)

⋅ ⋅ = = = = ⋅ ⋅ (2.44)

When the system transmit power is normalized to one, then the noise power _σ2

corresponding to a specific E N_{b 0} can be generated by

2 0 b t N E N M σ = ⋅ ⋅ (2.45)

where E_s is the symbol energy, T_s is the symbol duration, B is the system bandwidth, and M is the modulation order.

In the first simulation, the capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading SIMO channels with different numbers of receive antennas is examined. The results shown in Fig. 2.7 indicate that the channel capacity improves as more receive antennas are deployed. The ergodic channel capacity has a logarithmic increase when increasing the number of antennas at the receiving end.

In the second simulation, the capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading MISO channels with different numbers of transmit

antennas is examined. The results shown in Fig. 2.8 have the same trends as those shown in Fig. 2.7. When more transmit antennas are deployed, the channel capacity also has a logarithmic increasing improvement. However, the ergodic capacity of MISO channels is smaller than that of SIMO channels because the channel energy can not be combined coherently in the MISO channel case. In other words, the array gain is absent in the MISO channel case.

In the third simulation, the capacity of a SISO channel compared to the ergodic capacity of Rayleigh fading MIMO channels with different numbers of transmit and receive antennas is examined. The results shown in Fig. 2.9 indicate that the channel capacity increases linearly with the minimum number of transmit and receive antennas rather than logarithmically. Owing to the use of diversity at both transmitter and receiver, the capacity of MIMO channels is larger than those of different channel scenarios such as SIMO, MISO, and SISO channels.

In the forth simulation, the ZF V-BLAST BER performance with ideal detection and cancellation is examined. The results shown in Fig. 2.10 indicate that the diversity gain increases as the number of effective transmit antennas decreases.

In the fifth simulation, the ZF V-BLAST BER performance with the error propagation is examined. The results shown in Fig. 2.11 indicate that the BER performance will suffer from error propagation and the diversity gain degrades. The error propagation phenomenon will limit the performance because there are no preliminary decisions available to increase the reliability of the symbols detected and used for canceling in the interference cancellation step.

2.5 Summary

Information theory shows that multiple-input multiple-output (MIMO) communication systems can significantly increase the capacity of band-limited wireless channels by a factor of the minimum number of transmit and receive antennas, provided that a rich multipath scattering environment is utilized. In Sections 2.1 and 2.2, MIMO system model and MIMO channel capacity are introduced.

In order to achieve extraordinary data rate in MIMO systems, spatial multiplexing technique is presented in Section 2.3. Spatial multiplexing allows a data rate enhancement in a wireless radio link without additional power or bandwidth consumption. It is realized by transmitting independent data signals from the individual transmit antennas. Two typical spatial multiplexing schemes, D-BLAST and V-BLAST, are introduced in Sections 2.3.1 and 2.3.2.

( )

t

=

( )

t

+

( )

t

y

Hx

n

1 2 ( )

( )

( )

( )

t N t

x t

x t

x

t





























x

#



 

Rich Scattering Environment 11

h

21

h

1N_t

h

r t N N

h

1

( )

n t

2

( )

n t

( )

r N

n t

1 2 ( )

( )

( )

( )

r N t

y t

y t

y

t





























y

#



 

Transmitter Receiver

( )

t

=

( )

t

+

( )

t

y

Hx

n

1 2 ( )

( )

( )

( )

t N t

x t

x t

x

t





























x

#



 

Rich Scattering Environment 11

h

21

h

1N_t

h

r t N N

h

21

h

1N_t

h

r t N N

h

1

( )

n t

2

( )

n t

( )

r N

n t

1 2 ( )

( )

( )

( )

r N t

y t

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#



 

Transmitter Receiver

Figure 2.1: MIMO wireless transmission system model.

Transmitter Receiver

1 : 3 DEMUX Input Bits Encoder α Encoder β Encoder γ

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1 3

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2 4

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3 5

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1 4

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2 5

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3 6

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0

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Encoder α Encoder β Encoder γ 1 5

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1 6

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2 6

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2 7

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3 7

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3 8

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"

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Space Time Layer Decision ( Decoding ) Data Rate N∝   1 : 3 DEMUX Input Bits Encoder α Encoder β Encoder γ

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2 5

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3 6

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Encoder α Encoder β Encoder γ 1 5

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1 6

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2 6

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2 7

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Space Time Layer Decision ( Decoding ) Data Rate N∝  

Figure 2.3: Diagonal Bell Labs’ Layered Space-Time encoding procedure. 1. 2. 3. 4. 5. 6. Nulled Detected Detected Nulled Detected Cancelled Decode 1. 2. 3. 4. 5. 6. Nulled Detected Detected Nulled Detected Cancelled Decode